Kim Kardashian is becoming the fairy godmother of prison inmates, because they're flooding her inbox with thousands of letters every day ... asking her to help them find freedom.

Sources close to Kim tell TMZ ... inmates around the country are sending Kim an endless amount of notes from prison, hoping she and her legal team can find a way to get them clemency.

We're told Kim's also earned a new nickname within the prison system, as both staffers and inmates refer to her as "The Princess of Prison Reform.' The nickname and letters have some basis in fact ... Kim and her team just helped Cyntoia Brown get clemency in Tennesseeafter 15 years in prison.